With the advent of inexpensive digital color printers, methods and systems of color digital halftoning have become increasingly important in the reproduction of printed or displayed images possessing continuous color tones. It is well understood that most digital color printers operate in a binary mode, i.e., for each color separation, a corresponding color spot is either printed or not printed at a specified location or pixel. Digital halftoning controls the printing of color spots, where the spatial averaging of the printed color spots by either a human visual system or a viewing instrument, provides the illusion of the required continuous color tones.
The most common halftone technique is screening, which compares the required continuous color tone level of each pixel for each color separation with one or more predetermined threshold levels. The predetermined threshold levels are typically defined for a rectangular cell that is tiled to fill the plane of an image, thereby forming a halftone screen of threshold values. At a given pixel if the required color tone level is darker than the threshold halftone level, a color spot is printed at that specified pixel. Otherwise the color spot is not printed. The output of the screening process is a binary pattern of multiple small “dots”, which are regularly spaced as is determined by the size, shape, and tiling of the halftone cell. In other words, the screening output, as a two-dimensionally repeated pattern, possesses two fundamental spatial frequencies, which are completely defined by the geometry of the halftone screen.
It is understood in the art that the distribution of printed pixels depends on the design of the halftone screen. For clustered-dot halftone screens, all printed pixels formed using a single halftone cell typically group into one or more clusters. If a halftone cell only generates a single cluster, it is referred to as a single-dot halftone or single-dot halftone screen. Alternatively, halftone screens may be dual-dot, tri-dot, quad-dot, or the like.
While halftoning is often described in terms of halftone dots, it should be appreciated that idealized halftone dots can possess a variety of shapes that include rectangles, squares, lines, circles, ellipses, “plus signs”, X-shapes, pinwheels, and pincushions, and actual printed dots can possess distortions and fragmentation of those idealized shapes introduced by digitization and the physical printing process. Various digital halftone screens having different shapes and angles are described in: “An Optimum Algorithm for Halftone Generation for Displays and Hard Copies”, by T. M. Holladay, Proceedings of the Society for Information Display (Proc. SID), Vol. 21, No. 2, pp. 185 (1980).
A common problem that arises in digital color halftoning is the manifestation of moiré patterns. Moiré patterns are undesirable interference patterns that occur when two or more color halftone separations are printed over each other. Since color mixing during the printing process is a non-linear process, frequency components other than the fundamental frequencies and harmonics of the individual color halftone separations can occur in the final printout. For example, if an identical halftone screen is used for two color separations, theoretically, there should be no moiré patterns. However, any slight misalignment between the two color halftone separations occurring from an angular difference and/or a scalar difference will result in two slightly different fundamental frequency vectors. Due to nonlinear color mixing the difference in frequency vectors produces a beat frequency which will be visibly evident as a very pronounced moiré interference pattern in the output. Additionally, lateral displacement misregistration can result in significant color shifts if an identical halftone screen is used for two color separations. To avoid, for example, two-color moiré patterns and other color shifts due to misalignment and misregistration, or for other reasons, different halftone screens are commonly used for different color separations, where the fundamental frequency vectors of the different halftone screens are separated by relatively large angles. Therefore, the frequency difference between any two fundamental frequencies of the different screens will be large enough so that no visibly objectionable moiré patterns are produced.
In selecting different halftone screens, for example for three color separations, it is desirable to avoid any two-color moiré as well as any three-color moiré. It is well known that in the traditional printing industry that three halftone screens, which can be constructed by halftone cells that are square in shape and identical, can be placed at 15°, 45°, and 75°, respectively, from a point and axis of origin, to provide the classical three-color moiré-free solution. This is described in “Principles of Color Reproduction”, by J. A. G. Yule, John Wiley & Sons. N.Y. (1967).
However, for digital halftoning, the freedom to rotate a halftone screen is limited by the raster structure, which defines the position of each pixel. Since) tan(15°) and tan(75°) are irrational numbers, rotating a halftone screen to 15° or 75° cannot be implemented exactly in digital halftoning. To this end, some methods have been proposed to provide approximate instead of exact moiré-free solutions. For example, in U.S. Pat. No. 5,323,245, entitled: “Perpendicular, Unequal Frequency Non-Conventional Screen Patterns For Electronic Halftone Generation”, and in U.S. Pat. No. 5,583,660, entitled: “Non-Perpendicular, Equal Frequency Non-Conventional Screen Patterns For Electronic Halftone Generation”, this problem is approached by using a combination of two or more perpendicular, unequal frequency screen patterns and non-perpendicular, equal frequency non-conventional screen patterns. However, all these approximate solutions result in some halftone dots having centers that do not lie directly on addressable points, or on the pixel positions defined by the raster structure. Therefore, the shape and center location varies from one halftone dot to another. Consequently, additional interference or moiré between the screen frequencies and the raster frequency can occur. In another approach, U.S. Pat. No. 5,371,612, entitled: “Method Of And Apparatus For Forming Halftone Images” discloses a moiré prevention method to determine screen angles and sizes that is usable solely for square-shaped, halftone screens.
U.S. Pat. No. 6,798,539, entitled: “Method For Moiré-Free Color Halftoning Using Non-Orthogonal Cluster Screens” to Wang et al., discloses methods for using single-cell, non-orthogonal clustered-dot screens to satisfy the moiré-free conditions for color halftoning. The disclosure also provides methods that combine single-cell non-orthogonal clustered-dot screens and line screens for moiré-free color halftoning. Particularly, the selection of these single-cell halftone screens is determined by satisfying moiré-free conditions provided in the respective spatial or frequency equations. U.S. Pat. No. 6,798,539 to Wang et al. provides a background basis for the disclosure as taught in the specification which follows below, and as such it, as well as all of the above cited patents are hereby incorporated in their entirety for their teachings.
The difficulty in avoiding moiré between halftone screens is further exacerbated by the common practice of printing four colors. Four-color printing typically employs halftoning methods for the yellow image separation that produce less than optimal image quality. Typical clustered-dot methods often possess some residual moiré. The typical clustered-dot yellow configuration assumes square halftone cells and places yellow at 0° with a frequency that is ≈10% higher than the other screens. Low contrast moiré can be seen in many printed images for certain combinations of yellow and other colorants. Another common configuration for yellow utilizes a stochastic screen or error diffusion for yellow. That configuration results in a high degree of instability when used on many different printers. The result is inconsistency of color page-to-page and non-uniformity of color within a page.